There are two numbers such that the sum of the first and three times the second is 53, while difference between 4 times the first and twice the second is 2. What is the first number?
- 8
- 6
- 7
- None of these
Explanation
Given the equations:
x + 3y = 53 ... (1)
4x - 2y = 2 ... (2)
We can solve these equations using substitution or elimination. Let's use elimination.
Multiplying equation (1) by 2 and equation (2) by 3 to eliminate y:
2x + 6y = 106
12x - 6y = 6
Adding both equations:
14x = 112
x = 8
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- 10x = - 3
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